Question

Неподвижная ракета на Земле имеет длину 300 м. Если с точки зрения наблюдателя, оставшегося на Земле, при равномерном движении ее длина уменьшилась в 2 раза, то скорость ракеты равна..?

Answer 1

L=l0sqr((1-(v/c)^2)
l=300/2=150
l0=150
отсюда
v/c=sqr(4/9)приблизительно равно 0,66
ответ 0,63

Answer 2

Calculation of Rocket Speed

To calculate the speed of the rocket, we can use the concept of length contraction in special relativity. According to the question, the length of the rocket as observed by an observer on Earth has decreased by a factor of 2.

Let's assume the original length of the rocket is L and the observed length is L'. According to the length contraction formula, the observed length is given by:

L' = L * sqrt(1 - (v^2/c^2))

Where: - L is the original length of the rocket (300 m in this case) - v is the velocity of the rocket - c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)

We are given that the observed length has decreased by a factor of 2. Therefore, we can write:

L' = L/2

Substituting the values into the length contraction formula, we get:

L/2 = L * sqrt(1 - (v^2/c^2))

Simplifying the equation, we can solve for v:

sqrt(1 - (v^2/c^2)) = 1/2

Squaring both sides of the equation, we get:

1 - (v^2/c^2) = 1/4

Rearranging the equation, we have:

(v^2/c^2) = 3/4

Taking the square root of both sides, we get:

v/c = sqrt(3/4)

Simplifying further, we have:

v/c = sqrt(3)/2

Now, we can solve for the velocity of the rocket:

v = c * sqrt(3)/2

Substituting the value of the speed of light (c ≈ 3 x 10^8 m